The odds that A speaks the truth are 3:2 and the odds that B speaks the truth 5:3. In what percentage of cases are they likely to contradict each other on an identical point?
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Given,
P( A speaks truth ) = 3/(3 + 2) = 3/5
P( A speaks lie) = 1 - P(A speaks truth) = 1 - 3/5 = 2/5
P( B speaks truth ) = 5/(5 + 3) = 5/8
P( B speaks lie) = 1 - P( B speaks truth) = 1 - 5/8 = 3/8
They will contradict when A speaks truth , B speaks lie or B speaks truth , A speaks lie.
∴ probability = P(A speaks truth).P(B speaks lie) + P(A speaks lie).P(B speaks truth)
= 3/5 × 3/8 + 2/5 × 5/8
= 9/40 + 10/40 = 19/40 = 0.475
Hence, % of cases are they likely to contradict each other = 100 × Probability
= 100 × 0.475 = 47.5 %
P( A speaks truth ) = 3/(3 + 2) = 3/5
P( A speaks lie) = 1 - P(A speaks truth) = 1 - 3/5 = 2/5
P( B speaks truth ) = 5/(5 + 3) = 5/8
P( B speaks lie) = 1 - P( B speaks truth) = 1 - 5/8 = 3/8
They will contradict when A speaks truth , B speaks lie or B speaks truth , A speaks lie.
∴ probability = P(A speaks truth).P(B speaks lie) + P(A speaks lie).P(B speaks truth)
= 3/5 × 3/8 + 2/5 × 5/8
= 9/40 + 10/40 = 19/40 = 0.475
Hence, % of cases are they likely to contradict each other = 100 × Probability
= 100 × 0.475 = 47.5 %
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